1. Field of the Invention
The present invention relates generally to computerized simulation of hydrocarbon reservoirs, and, more particularly, to a method and data system of 2.5D unstructured grid storage, calculation, and visualization.
2. Description of Related Art
[1] A subterranean geologic body or formation contains multi-phase, multi-component fluids, and accordingly a petroleum reservoir may contain oil, natural gas, water and several constituent compounds, that may be modeled to predict the fluid flow from a reservoir, which is also known as reservoir simulation. Reservoir simulation models may be run before or after a well is drilled to determine production rate, etc. for the various methods.
Current reservoir modeling techniques create a numerical grid of the reservoir comprised of a plurality of grid cells, and process data in the finite volume of each grid cell. Because reservoirs can be complex, and grid cells can number in the millions, the simulation models can take days. Accordingly, Saudi Aramco's POWERS™ program was created to streamline data processing using parallel computing. Parallel computing, as performed by the POWERS program, divides the numerical grid into a plurality of domains, with each domain consisting of a plurality of grid cells. If the numerical grid is a structured grid, meaning each grid cell can be described the same, i.e., each inner vertex is incident to a fixed number of cells and each cell is defined by a fixed number of faces and edges. Structured grids may use Cartesian coordinates (I,J,K), FIGS. 1 and 2, or some other similar mapping method to locate grid cells for data processing, such as corner point geometry format shown in FIGS. 3 and 4.
To run the simulations using structured grids, rock properties, described using geologic models (porosity, permeability, etc.) as well as the geometry of the rock formation and data related to the well bore, are read into each computer. Because the domain is sub-divided into several finite volumes, or grid cells, conservation equations of mass, momentum, and energy are then constructed for each grid cell. These balance equations represent the discrete time rate of change of these quantities stored in the grid block due to the inter-block fluxes and sources and sinks of the quantities due to the physical and chemical processes being modeled, and are accordingly a set of discrete non-linear partial differential equations involving complex functions. Finally, using the mapping method for the grid, each computer can arrange for cross talk with other computers to simulate flow through the domains.
Unfortunately, reservoirs are of a sedimentary origin and have multiple layers that have thicknesses and depth variations throughout, which do not neatly follow the pattern of a structured grid. For example, a layer can disappear locally due to lack of deposition or subsequent erosion, which is known as a pinch-out. Also, uplifting (the raising of the earth's crust) and subsidence (the lowering of the earth's crust) over geologic time can lead to faulting and fracturing of the layers. In addition to the complexity of the reservoir layers, complex wells may be drilled into the reservoirs to extracts fluids from them or to inject fluids into them for pressure maintenance or enhance-oil-recovery operations, i.e., these wells may be multi-branched as shown in FIG. 5. Conventional reservoir simulators that use Cartesian grids or corner point geometry (CPG) grids for reservoir simulation have difficulty, with complex geological features (including faults, pinch-outs, and, erosion) and complex well geometries (including deviated or multi-lateral wells) as shown in FIG. 6, and may generate smaller grid dimensions to account for these features. With conventional techniques, smaller grid dimensions result in more accurate approximations of the reservoir, but at a cost of larger datasets (i.e., more data points). In addition, as shown in FIG. 7, local grid refinement (LGR) may be used to account for geological features when using structured grids. LGR involves splitting particular cells into multiple, smaller cells to better model the underlying continuous real geometry, at a cost of complexity and more data points. To reduce complexity of the grid, unstructured grids, built to represent the geologic layers and well geometry would be better.
To create unstructured grids, oil or gas reservoirs are subdivided into non-uniform elementary finite-volumes, i.e., grid cells or grid blocks. These grid cells can have variable numbers of faces and edges that are positioned to honor physical boundaries of geological structures and well geometry embedded within the reservoir. Accordingly, these maps may be very complex. Examples of unstructured gridding methods includes Voronoi diagrams, i.e., a grid where each cell has faces and edges that are closer to one Voronoi site or point than any other Voronoi site or point. While unstructured grids more accurately reflect the geological features of the geological body, in order to perform unstructured grid simulation using parallel processing techniques, the global coordinate system, e.g., (I,J,K) Cartesian indexing, must be replaced with a global hash table, accessible by the computer processing each domain, to arrange for cell and domain cross-talk. Unfortunately, the global hash table for a model with, e.g., millions of cells, can overwhelm the memory of for each of the parallel computers.
In addition to the problems with prior art reservoir grids, simulating reservoirs having multi-lateral wells require more data input and use more complex algorithms, and simulation models for this types of production methods can be very cumbersome—even using the POWERS™ system. The computational complexity of these equations is further complicated by geological model size is typically in the tens of million to hundreds of million of grid cells. Since finding a solution to millions of partial differential equations is computationally expensive, reservoir simulation models are usually built at a coarser scale than the geologic model via a data process known as upscaling, i.e. the averaging of rock properties for a plurality of grid cells. While computationally more efficient, upscaling renders the simulation model less accurate (and the upscaling makes the inaccuracy of the structured grid models more pronounced).
Therefore, the machine, methods, and program products of this invention constitute the enabling technology to process a 2.5 dimensional unstructured grids for complex reservoirs and multi-lateral well simulations to more accurately approximate well and geological features and reduce the computational complexity of the simulation.